Wormholes with a barotropic equation of state admitting a one-parameter group of conformal motions

TL;DR

This paper explores how a linear barotropic equation of state influences the construction of traversable wormholes, showing that conformal symmetry conditions allow for consistent solutions when <-1, linking to phantom dark energy.

Contribution

It demonstrates that wormholes with conformal motions can be constructed under a linear barotropic equation of state with <-1, providing new conditions for their existence.

Findings

Redshift and shape functions exist for <-1 under conformal symmetry.

The equation of state <-1 is compatible with traversable wormholes.

Conformal motions facilitate wormhole solutions with specific matter conditions.

Abstract

The theoretical construction of a traversable wormhole proposed by Morris and Thorne maintains complete control over the geometry by assigning both the shape and redshift functions, thereby leaving open the determination of the stress-energy tensor. This paper examines the effect of introducing the linear barotropic equation of state $p_r=\omega\rho$ on the theoretical construction. If either the energy density or the closely related shape function is known, then the Einstein field equations do not ordinarily yield a finite redshift function. If, however, the wormhole admits a one-parameter group of conformal motions, then both the redshift and shape functions exist provided that $\omega <-1$. In a cosmological setting, the equation of state $p=\omega\rho$, $\omega <-1$, is associated with phantom dark energy, which is known to support traversable wormholes.